At \({K}= 3\)  the closed-form solution of the
GSP
recurrences
was given in [1]}. For methodical
purposes it still makes sense to start the presentation of
this solution
by the tutorial re-derivation of the
first nontrivial \({K}=3\)  ISP
pattern.
Indeed, in our present notation
the correspondence between \({\cal H}_{phys}\)  and
\({\cal H}_{math}\) 
can be seen as mediated either by a single-step
simplification
of the inner product
\(\langle _{[0]} \psi _a|\psi _b\rangle \ \rightarrow \ \langle _{} \psi _a|\psi _b\rangle \)  (at \(K=2\) ), or by a two-step
realization in which the preparatory step
\(\langle _{[0]} \psi _a|\psi _b\rangle \ \rightarrow \ \langle _{[1]} \psi _a|\psi _b\rangle \)  is followed by the final step
\(\langle _{[1]} \psi _a|\psi _b\rangle \ \rightarrow \ \langle _{} \psi _a|\psi _b\rangle \)  (at \(K=3\) ).
